Quantum Mechanical Description Research Articles

Signatures of long-range spin-spin interactions in an (In,Ga)As quantum dot ensemble

We present an investigation of the electron spin dynamics in an ensemble of singly-charged quantum dots subject to an external magnetic field and laser pumping with circularly polarized light. The spectral laser width is tailored such that different groups of quantum dots are coherently pumped. Surprisingly, the dephasing time $T^*$ of the electron spin polarization depends only weakly on the laser spectral width. These findings can be consistently explained by a cluster theory of coupled quantum dots with a long range electronic spin-spin interaction. We present a numerical simulation of the spin dynamics based on the central spin model that includes a quantum mechanical description of the laser pulses as well as a time-independent Heisenberg interaction between each pair of electron spins. We discuss the individual dephasing contributions stemming from the Overhauser field, the distribution of the electron $g$-factors and the electronic spin-spin interaction as well as the spectral width of the laser pulse. This analysis reveals the counterbalancing effect of the total dephasing time when increasing the spectral laser width. On one hand, the deviations of the electron $g$-factors increase. On the other hand, an increasing number of coherently pumped electron spins synchronize due to the spin-spin interaction. We find an excellent agreement between the experimental data and the dephasing time in the simulation using an exponential distribution of Heisenberg couplings with a mean value $\overline{J}\approx 0.26\,\mathrm{\mu eV}$.

Dark Plasmon Modes in Symmetric Gold Nanoparticle Dimers Illuminated by Focused Cylindrical Vector Beams

The plasmon hybridization model of electromagnetic coupling between plasmonic nanoparticles predicts the formation of lower energy “bonding” and higher energy “antibonding” modes in analogy with the quantum mechanical description of chemical bonding. For a symmetric metallic nanoparticle dimer excited by linearly polarized light, the hybridization picture predicts that in-phase coupling of the dipole moments is optically allowed, creating bright “modes”, whereas the out-of-phase coupling is dark due to the cancellation of the oppositely oriented dipole moments (in the quasistatic approximation). These bright modes are electric dipolar in nature and readily couple to scalar (i.e., linearly or circularly polarized) beams of light. We show that focused cylindrical vector beams, specifically azimuthally and radially polarized beams, directly excite dark plasmon modes in symmetric gold nanoparticle (AuNP) dimers at normal incidence. We use single-particle spectroscopy and electrodynamics simulations to study the resonance scattering of AuNP dimers illuminated by azimuthally and radially polarized light. The electric field distributions of the focused azimuthal or radial beams are locally polarized perpendicular or parallel to the AuNP dimer axis, but with opposite directions at each particle. Therefore, the associated combinations of single-particle dipole moments are out-of-phase, and the excitation (resonance) is of so-called “dark modes”. In addition, multipole expansion of the fields associated with each scattering spectrum shows that the vector beam excitation involves driving multipolar, e.g., magnetic dipolar and electric quadrupolar, modes, and that they even dominate the scattering spectra (vs electric dipole). This work opens new opportunities for investigating dark plasmon modes in nanostructures, which are difficult to selectively excite by conventional polarized light.

A Quantum-Mechanical Map for Bonding and Properties in Solids.

A 2D map is created for solid-state materials based on a quantum-mechanical description of electron sharing and electron transfer. This map intuitively identifies the fundamental nature of ionic, metallic, and covalent bonding in a range of elements and binary compounds; furthermore, it highlights a distinct region for a mechanism recently termed "metavalent" bonding. Then, it is shown how this materials map can be extended in the third dimension by including physical properties of application interest. Finally, it is shown how the map coordinates yield new insight into the nature of the Peierls distortion in phase-change materials and thermoelectrics. These findings and conceptual approaches provide a novel avenue to tailor material properties.

Time in quantum mechanics: A fresh look at the continuity equation

The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock. We consider what happens when this classical time is replaced by a non-relativistic quantum-mechanical description of the clock. From the clock-dependent Schr\"odinger equation (as analogue of the time-dependent Schr\"odinger equation) we derive a continuity equation, where, instead of a time-derivative, an operator occurs that depends on the flux (probability current) density of the clock. This clock-dependent continuity equation can be used to analyze the dynamics of a quantum system and to study degrees of freedom that may be used as internal clocks for an approximate description of the dynamics of the remaining degrees of freedom. As an illustration, we study a simple model for coupled electron-nuclear dynamics and interpret the nuclei as quantum clock for the electronic motion. We find that whenever the Born-Oppenheimer approximation is valid, the continuity equation shows that the nuclei are the only relevant clock for the electrons.

Autonomous Quantum Machines and Finite-Sized Clocks

Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise amount of time, using a classical clock. A fully quantum mechanical description of such a device would include a quantum description of the clock whose state is generally disturbed because of the back-reaction on it. Such a description is needed if we wish to consider finite sized autonomous quantum machines requiring no external control. The extent of the back-reaction has implications on how small the device can be, on the length of time the device can run, and is required if we want to understand what a fully quantum mechanical treatment of an observer would look like. Here, we consider the implementation of a unitary by a finite sized device which we call the "Quasi-Ideal clock", and show that the back-reaction on it can be made exponentially small in the device's dimension with only a linear increase in energy. As a result, an autonomous quantum machine need only be of modest size and or energy. We are also able to solve a long-standing open problem by using a finite sized quantum clock to approximate the continuous evolution of an Idealised clock. The result has implications on the equivalence of different paradigms of quantum thermodynamics, some which allow external control and some which only allow autonomous thermal machines.

Magnetic field dependence of the electron spin revival amplitude in periodically pulsed quantum dots

Periodic laser pulsing of singly charged semiconductor quantum dots in an external magnetic field leads to a synchronization of the spin dynamics with the optical excitation. The pumped electron spins partially rephase prior to each laser pulse, causing a revival of electron spin polarization with its maximum at the incidence time of a laser pulse. The amplitude of this revival is amplified by the frequency focusing of the surrounding nuclear spins. Two complementary theoretical approaches for simulating up to 20 million laser pulses are developed and employed that are able to bridge between 11 orders of magnitude in time: a fully quantum mechanical description limited to small nuclear bath sizes and a technique based on the classical equations of motion applicable for a large number of nuclear spins. We present experimental data of the nonmonotonic revival amplitude as function of the magnetic field applied perpendicular to the optical axis. The dependence of the revival amplitude on the external field with a profound minimum at $4\;$T is reproduced by both of our theoretical approaches and is ascribed to the nuclear Zeeman effect. Since the nuclear Larmor precession determines the electronic resonance condition, it also defines the number of electron spin revolutions between pump pulses, the orientation of the electron spin at the incidence time of a pump pulse, and the resulting revival amplitude. The magnetic field of $4\;$T, for example, corresponds to half a revolution of nuclear spins between two laser pulses.

Pre-Born–Oppenheimer molecular structure theory

ABSTRACTIn pre-Born–Oppenheimer (pre-BO) theory a molecule is considered as a quantum system as a whole, including the electrons and the atomic nuclei on the same footing. This approach is fundamentally different from the traditional quantum chemistry treatment, which relies on the separation of the motion of the electrons and the atomic nuclei. A fully quantum mechanical description of molecules has a great promise for future developments and applications. Its most accurate versions may contribute to the definition of new schemes for metrology and testing fundamental physical theories; its approximate versions can provide an efficient theoretical description for molecule-positron interactions and, in general, it would circumvent the tedious computation and fitting of potential energy surfaces and non-adiabatic coupling vectors while it includes also the quantum nuclear motion also often called ‘molecular quantum dynamics’. To achieve these goals, the review points out important technical and fundamental open questions. Most interestingly, the reconciliation of pre-BO theory with the classical chemistry knowledge touches upon fundamental problems related to the measurement problem of quantum mechanics.

First-Principles Modeling in Heterogeneous Electrocatalysis

The last decade has witnessed tremendous progress in the development of computer simulation based on quantum mechanical description of the interactions between electrons and between electrons and atomic nuclei with electrode potentials taken into account–promoting the possibility to model electrocatalytic reactions. The cornerstone of this development was laid by the widely used computational hydrogen electrode method which involves a posteriori correction of standard constant charge first principles studies in solvent environment. The description of this technique and its contribution to our effort to understand electrocatalytic reactions on the active sites of metal-based nanoparticles are reviewed. The pathways and energetics of the relevant elementary reactions are presented. We also discussed a recent attempt in the literature to account for the inflow and outflow of electrons from the electrode as electrochemical reactions proceed, which has been greatly assisted by the development of density functional theory within the grand canonical framework. Going beyond the computational hydrogen electrode method by explicit incorporation of electrode potential within the calculations permits access to more detailed insights without requiring extra computational burden.

An Ab Initio QM/MM Study of the Electrostatic Contribution to Catalysis in the Active Site of Ketosteroid Isomerase.

The electric field in the hydrogen-bond network of the active site of ketosteroid isomerase (KSI) has been experimentally measured using vibrational Stark effect (VSE) spectroscopy, and utilized to study the electrostatic contribution to catalysis. A large gap was found in the electric field between the computational simulation based on the Amber force field and the experimental measurement. In this work, quantum mechanical (QM) calculations of the electric field were performed using an ab initio QM/MM molecular dynamics (MD) simulation and electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method. Our results demonstrate that the QM-derived electric field based on the snapshots from QM/MM MD simulation could give quantitative agreement with the experiment. The accurate calculation of the electric field inside the protein requires both the rigorous sampling of configurations, and a QM description of the electrostatic field. Based on the direct QM calculation of the electric field, we theoretically confirmed that there is a linear correlation relationship between the activation free energy and the electric field in the active site of wild-type KSI and its mutants (namely, D103N, Y16S, and D103L). Our study presents a computational protocol for the accurate simulation of the electric field in the active site of the protein, and provides a theoretical foundation that supports the link between electric fields and enzyme catalysis.

Proca Particle in Riemannian Spacetimes

Relativistic quantum-mechanical description of electromagnetic, inertial, and gravitational interactions of a Proca (spin-1) particle is presented. Covariant equations defining electromagnetic interactions of a Proca particle with the anomalous magnetic and electric dipole moments in Riemannian spacetimes are formulated. The relativistic Foldy–Wouthuysen transformation with allowance for only terms proportional to the zero power of the Planck constant is performed as an example. The Hamiltonian obtained agrees with the corresponding Hamiltonians derived for scalar and Dirac particles and with their classical counterpart.

Spectral Faraday rotation in tripyridinium bis[tetrachloroferrate(III)] chloride molecular magnet at room temperature due to electronic transition

The physical mechanism responsible for Faraday rotation (FR) in magnetic molecules under the irradiation of visible light is under intense investigations. In this paper, a quantum mechanical description of the Faraday rotation is provided based on the electronic transitions between the molecular states. The method is applied on bis[tetrachloroferrate(III)]chloride magnetic molecule showing significant FR under irradiation of the visible light (λ=[450,775]nm) at room temperature. Use of dielectric tensor for the molecule in terms of oscillator strengths between HOMOs (highest occupied molecular orbital) and LUMOs (lowest unoccupied molecular orbital) leads to magnetization curve as a function of frequency. The results are obtained in view of quantitative ab initio simulation of electronic structure in the framework of density functional theory (DFT), and the wave functions are calculated making use of Gaussian 03 software within the scheme of B3LYP hybrid functional approximation. The simulation method works for discrete molecules in acetonitrile solvent and considers effect of the solvent as well. The refractive index and the oscillator strengths between molecular states are calculated using the simulated wave functions and the angle of rotation versus wavelength is presented. Comparison of the theoretical results with those of the experiment justifies reasonably the role of electronic transitions between molecular states which have not been emphasized as a mechanism of Faraday rotation in iron-based complexes.

Electronic stopping power from time-dependent density-functional theory in Gaussian basis

The electronic stopping power, which is the energy transfer from a charged particle travelling through a material to the electrons of the material, has attracted much attention back from the early beginnings of quantum mechanics. It requires the description of the electronic excitations taking place in the target material and has been limited to model systems for a long time. With the advent of time-dependent density-functional theory (TDDFT), it is nowadays possible to provide a complete and realistic quantum-mechanical description of the phenomenon. We present here an implementation of TDDFT based on Gaussian basis for finite systems. The localized Gaussian basis has numerous advantages, such as the cheap account of core electrons, the simple implementation of the modern hybrid functionals, and the possibility of a tunable basis accuracy as a function of space. With our tool, we explore the bulk limit, the validity of the impact parameter averaging to obtain the experimental random electronic stopping power, and the connection to the simpler linear-response results for lithium metallic clusters for different ionic projectiles.

Obtaining the non-relativistic quantum mechanics from quantum field theory: issues, folklores and facts

Given the classical dynamics of a non-relativistic particle in terms of a Hamiltonian or an action, it is relatively straightforward to obtain the non-relativistic quantum mechanics (NRQM) of the system. These standard procedures, based on either the Hamiltonian or the path integral, however, do not work in the case of a relativistic particle. As a result we do not have a single-particle description of relativistic quantum mechanics (RQM). Instead, the correct approach requires a transmutation of dynamical variables from the position and momentum of a single particle to a field and its canonical momentum. Particles, along with antiparticles, reappear in a very nontrivial manner as the excitations of the field. The fact that one needs to adopt completely different languages to describe a relativistic and non-relativistic free particle implies that obtaining the NRQM limit of QFT is conceptually nontrivial. I examine this limit in several approaches (like, for e.g., Hamiltonian dynamics, Lagrangian and Hamiltonian path integrals, field theoretic description etc.) and identify the precise issues which arise when one attempts to obtain the NRQM from QFT in each of these approaches. The dichotomy of NRQM and QFT does not originate just from the square root in the Hamiltonian or from the demand of Lorentz invariance, as is sometimes claimed. The real difficulty has its origin in the necessary existence of antiparticles to ensure a particular notion of relativistic causality. Because of these conceptual issues, it turns out that one cannot, in fact, obtain some of the popular descriptions of NRQM by any sensible limiting procedure applied to QFT. To obtain NRQM from QFT in a seamless manner, it is necessary to work with NRQM expressed in a language closer to that of QFT. This fact has several implications, especially for the operational notion of space coordinates in quantum theory. A close examination of these issues, which arise when quantum theory is combined with special relativity, could offer insights in the context of attempts to combine quantum theory with general relativity.

Effect of DNA Environment on Electronically Excited States of Methylene Blue Evaluated by a Three-Layered QM/QM/MM ONIOM Scheme.

Interactions between chromophores and biological environments may alter the electronic properties of the chromophores. A three-layered QM/QM/MM ONIOM scheme with electrostatic embedding is implemented to investigate the influence of an additional QM layer on excited-state calculations with respect to a standard QM/MM description. The implemented ONIOM scheme is employed to compute the electronic excitations of the photosensitizer methylene blue interacting with a solvated DNA double strand. It is shown that the additional quantum mechanical description of several nucleobases in the vertical energy calculations induces energy shifts in the excited states of methylene blue, compared to the energies of a traditional QM/MM scheme, where the solvated double strand is described fully classically. The energy shifts present an electrostatic component, caused by a charge redistribution of the environment, and an electronic-coupling component, originated by the mixing between the electronic bright state of methylene blue and a charge-transfer state between methylene blue and guanine. In addition, hydrogen bonding and stacking interactions are stronger when the environment is described quantum mechanically during the geometry optimizations than when it is fully described by molecular mechanics. These larger intermolecular interactions produce further energy shifts in the excitation energies of the photosensitizer.

Exciton Relaxation Cascade in two-dimensional Transition Metal Dichalcogenides

Monolayers of transition metal dichalcogenides (TMDs) are characterized by an extraordinarily strong Coulomb interaction giving rise to tightly bound excitons with binding energies of hundreds of meV. Excitons dominate the optical response as well as the ultrafast dynamics in TMDs. As a result, a microscopic understanding of exciton dynamics is the key for a technological application of these materials. In spite of this immense importance, elementary processes guiding the formation and relaxation of excitons after optical excitation of an electron-hole plasma has remained unexplored to a large extent. Here, we provide a fully quantum mechanical description of momentum- and energy-resolved exciton dynamics in monolayer molybdenum diselenide (MoSe2) including optical excitation, formation of excitons, radiative recombination as well as phonon-induced cascade-like relaxation down to the excitonic ground state. Based on the gained insights, we reveal experimentally measurable features in pump-probe spectra providing evidence for the exciton relaxation cascade.

Microscopic Linear Response Theory of Spin Relaxation and Relativistic Transport Phenomena in Graphene

We present a unified theoretical framework for the study of spin dynamics and relativistic transport phenomena in disordered two-dimensional Dirac systems with pseudospin-spin coupling. The formalism is applied to the paradigmatic case of graphene with uniform Bychkov-Rashba interaction and shown to capture spin relaxation processes and associated charge-to-spin interconversion phenomena in response to generic external perturbations, including spin density fluctuations and electric fields. A controlled diagrammatic evaluation of the generalized spin susceptibility in the diffusive regime of weak spin-orbit interaction allows us to show that the spin and momentum lifetimes satisfy the standard Dyakonov-Perel relation for both weak (Gaussian) and resonant (unitary) nonmagnetic disorder. Finally, we demonstrate that the spin relaxation rate can be derived in the zero-frequency limit by exploiting the SU(2) covariant conservation laws for the spin observables. Our results set the stage for a fully quantum-mechanical description of spin relaxation in both pristine graphene samples with weak spin-orbit fields and in graphene heterostructures with enhanced spin-orbital effects currently attracting much attention.

Quantum field-theoretical description of neutrino and neutral kaon oscillations

It is shown that the neutrino and neutral kaon oscillation processes can be consistently described in quantum field theory using only plane waves of the mass eigenstates of neutrinos and neutral kaons. To this end, the standard perturbative S-matrix formalism is modified so that it can be used for calculating the amplitudes of the processes passing at finite distances and finite time intervals. The distance-dependent and time-dependent parts of the amplitudes of the neutrino and neutral kaon oscillation processes are calculated and the results turn out to be in accordance with those of the standard quantum mechanical description of these processes based on the notion of neutrino flavor states and neutral kaon states with definite strangeness. However, the physical picture of the phenomena changes radically: now, there are no oscillations of flavor or definite strangeness states, but, instead of it, there is interference of amplitudes due to different virtual mass eigenstates.

Diffusion of helium, hydrogen and deuterium in diamond: Experiment, theory and geochemical applications

Diffusivities of helium, deuterium and hydrogen have been characterized in diamond. Polished CVD diamond was implanted with either 3He, 2H, or 1H. Implanted samples were sealed under vacuum in silica glass capsules, and annealed in 1-atm furnaces. 3He, 2H and 1H distributions were measured with Nuclear Reaction Analysis. We obtain these Arrhenius relations:DHe = 4.00 × 10−15 exp(−138 ± 14 kJ mol−1/RT) m2 s−1.D2H = 1.02 × 10−4 exp(−262 ± 17 kJ mol−1/RT) m2 s−1.D1H = 2.60 × 10−4 exp(−267 ± 15 kJ mol−1/RT) m2 s−1.Diffusivities of 1H and 2H agree within experimental uncertainties, indicating little diffusive mass fractionation of hydrogen in diamond.To complement the experimental measurements, we performed calculations using a first-principles quantum mechanical description of diffusion in diamond within the Density Functional Theory (DFT). Differences in 1H and 2H diffusivities from calculations are found to be ∼4.5%, reflected in differences in the pre-exponential factor. This small difference in diffusivities, despite the large relative mass difference between these isotopes, is due to the fact that the atomistic process involved in the transition along the diffusion pathway is dictated by local changes to the diamond structures rather than to vibrations involving 1H/2H. This finding is consistent with the experimental results given experimental uncertainties. In contrast, calculations for helium diffusion in diamond indicate a difference of 15% between diffusivities of 3He and 4He.Calculations of diffusion distances for hydrogen using our data yield a distance of 50 μm in diamond in 300,000 years at 500 °C and ∼30 min at 1400 °C. Diffusion distances for He in diamond are shorter than for H at all temperatures above ∼350 °C, but differences increase dramatically with temperature because of the higher activation energy for H diffusion. For example, a 50 μm diffusion distance for He would be attained in ∼40 Myr at 500 °C and 400 yr at 1400 °C. For comparison, a 50 μm diffusion distance for N in diamond would require nearly 1 billion years at 1400 °C.The experimental data indicate that diamonds equilibrate with ambient H and He in the mantle on timescales brief relative to most geological processes and events. However, He diffusion in diamond is slower than in any other mineral measured to date, including other kimberlite-hosted minerals. Under some circumstances, diamond may provide information about mantle He not recoverable from other minerals. One possibility is diamonds entrained in kimberlites. Since the ascent of kimberlite from the mantle to near-surface is very rapid, entrained diamonds may retain most or all of the H and He acquired in mantle environments. Calculations using reasonable ascent rates and T-t paths indicate that He diffusive loss from kimberlite-hosted diamonds is negligible for grains of 1.0–0.2 mm radius, with fractional losses <0.15% for all ascent rates considered. If the host kimberlite magma is effectively quenched in the near-surface (or is erupted), diamonds should contain a faithful record of [He] and He isotopes from the mantle source region. Preservation of H in kimberlite-hosted diamonds is less clear-cut, with model outcomes depending critically upon rates of ascent and cooling.

Relativistic entanglement

The relativistic quantum theory of Stueckelberg, Horwitz and Piron (SHP) describes in a simple way the experiment on interference in time of an electron emitted by femtosecond laser pulses carried out by Lindner et al. In this paper, we show that, in a way similar to our study of the Lindner et al. experiment (with some additional discussion of the covariant quantum mechanical description of spin and angular momentum), the experiment proposed by Palacios et al. to demonstrate entanglement of a two electron state, where the electrons are separated in time of emission, has a consistent interpretation in terms of the SHP theory. We find, after a simple calculation, results in essential agreement with those of Palacios et al.; but with the observed times as values of proper quantum observables.

Complexation reactions in pyridine and 2,6-dimethylpyridine-water system: The quantum-chemical description and the path to liquid phase separation.

Phase separation in substituted pyridines in water is usually described as an interplay between temperature-driven breakage of hydrogen bonds and the associating interaction of the van der Waals force. In previous quantum-chemical studies, the strength of hydrogen bonding between one water and one pyridine molecules (the 1:1 complex) was assigned a pivotal role. It was accepted that the disassembly of the 1:1 complex at a critical temperature leads to phase separation and formation of the miscibility gap. Yet, for over two decades, notable empirical data and theoretical arguments were presented against that view, thus revealing the need in a revised quantum-mechanical description. In the present study, pyridine-water and 2,6-dimethylpyridine-water systems at different complexation stages are calculated using high level Kohn-Sham theory. The hydrophobic-hydrophilic properties are accounted for by the polarizable continuum solvation model. Inclusion of solvation in free energy of formation calculations reveals that 1:1 complexes are abundant in the organically rich solvents but higher level oligomers (i.e., 2:1 dimers with two pyridines and one water molecule) are the only feasible stable products in the more polar media. At the critical temperature, the dissolution of the external hydrogen bonds between the 2:1 dimer and the surrounding water molecules induces the demixing process. The 1:1 complex acts as a precursor in the formation of the dimers but is not directly involved in the demixing mechanism. The existence of the miscibility gap in one pyridine-water system and the lack of it in another is explained by the ability of the former to maintain stable dimerization. Free energy of formation of several reaction paths producing the 2:1 dimers is calculated and critically analyzed.